In the electronics industry, thin-sliced wafers, such as wafers of high-purity semiconductors of silicon or germanium single crystals, are very important materials for the manufacture of various kinds of electronic elements, such as transistors, integrated circuits, oscillators, and the like. It is highly desirable in such wafer materials that the thickness, thickness variation, bowing of the wafers as well as the flatness of the wafer surface are strictly controlled with high precision.
In a conventional method, for example, as disclosed in Japanese Industrial Standard, H 0611-1971 "Methods of Measurement of Thickness, Taper and Bow for Silicon Wafers", the thickness or thickness variation of a wafer is determined by measuring thicknesses at several measuring points on the point-by-point basis. The thickness variation is usually expressed by the difference between the maximum value and the minimum value of thickness measured at 5 or more measuring points, which consist of the center point and points distributed in raidal symmetry around the center point and spaced several millimeters from the periphery of the wafer.
The point-by-point basis measurement is conventionally carried out by use of a plunger-type dial gauge, in which a wafer to be measured is mounted on an anvil and the surface of the wafer is contacted directly with the point of the probe of the dial gauge. Such direct contacting method is undesirable because the surface of the wafer eventually, though very sightly, becomes injured or contaminated by the direct contact of the probe point.
In order to avoid the above disadvantage encountered in the direct contacting method for the thickness measurement of a wafer, a non-contacting apparatus has recently been proposed (see U.S. Pat. No. 3,491,240), according to which, as the principle of measurement, a light beam is projected to a measuring point on the surface of the wafer, the reflected light beam is detected by a detector, and the intensity of the reflected light beam is converted to electric signals corresponding to the thickness of the wafer at the measuring point.
When the thickness variation of a wafer is to be determined, using either the contacting type or non-contacting type of apparatus, the thickness of the wafer is determined at several measuring points on the point-by-point basis, and the difference between the maximum and minimum values of the measured thicknesses is taken as the thickness variation. In this conventional measuring procedure, it is naturally required that the wafer should be moved horizontally to have all the predetermined measuring points, one by one, come exactly under the point of the fixed probe or light beam projector so that all of the measuring points can be measured for their thicknesses by a single probe or projector.
The handling of the wafer in the above movement is usually carried out by use of a sort of vacuum sucker, and yet there is the unavoidable danger that the surface of the wafer is scratched or contaminated as a result of contact with the vacuum sucker and the probe or projector and consequently in some cares the wafer itself becomes broken.
Further, the measuring operator is required to judge whether or not each wafer so examined has come up to the predetermined specifications promptly on the spot by comparing the maximum value and the minimum value of thickness measured point by point or the difference between those values and the predetermined standard values which the operator has committed to memory for each of the wafers. A manual operation of this nature is of course very laborious, and is apt to lead to serious errors in the work of wafer inspection even when the number of measuring points for each wafer is relatively small, say 5 or so.
The flatness of the surface of the semiconductor wafer has been required to be more and more critically perfect with the development of the electronics technology using silicon-made semiconductor wafers having a larger and larger diameter. In order to guarantee a very high precision for the surface flatness of polished silicon semiconductor wafers useful for integral circuits, the measurement of thicknesses at 5 or so measuring points may be insufficient, but the measurement conducted at measuring points distributed lattice-wise at small intervals throughout the surface of the wafer will be sufficient. For example, the thickness of a silicon wafer 3- to 5-inches in diameter may be measured at measuring points distributed lattice-wise on the surface longitudinally and laterally at regular intervals of one-fourth inch, the number of the measuring points per wafer being 100 to 200 or more.
It is almost a routine practice that the data of the above multi-point measurement of thickness, or rather the differences of the heights of the individual measuring points from a reference surface, which latter is determined with at least three measuring points, are used for the calculation of the value of non-linear thickness variation (NTV). NTV may be defined as the difference between the maximum height and the minimum height of the measuring points relative the reference surface. Such a multi-point measurement is practically impossible with the conventional point-by-point basis measuring apparatus which is not suitable for treating a large number of wafers.